Interpolation and Extrapolation, Business Mathematics and Statistics Video Lecture | Business Mathematics and Statistics - B Com

hey guys mr. Brian's here again and I'm
giving you guys a little video on
estimating values from graphs today and
as they actually have a couple of very
specific names and when we do that and
hopefully I'll say these correctly I
always get them wrong extrapolation and
interpolation so guys please if I say
these wrong please correct me and tell
me how to stay in say them but again not
a big deal if I do alrighty so let's
start with this first example X is equal
to 4 so if I look at down here X is
equal to 4 and I go up on my graph here
you see I have these data points here
that I plot it and I just drew a line
through and I go up until I hit the
graph and then I go to my y-axis
you'll see that at x equals 4 all the
way over Y is equal to 3 okay really
guys there's no estimating with that
it's just you know pretty much we know
the exact value because we have those
data points
okay so X is equal to 4 y must be 3 okay
it's pretty simple pretty
straightforward already so what about
this example five point one of these
straight lines on this one so if I look
at five point one will 5.1 I can't
exactly say well that's two so I'm going
to have the estimate here okay so I'm
going to have to estimate that five
point one is probably somewhere really
really close to here okay I'm actually
going to move that over just a smidge
okay so five point one is somewhere
right there
and then I go up until I hit the graph
just like before and then I go over here
till I hit the y-axis so what I'm doing
here is I'm estimating between these two
points okay between this point and
between this point okay I'm estimating
some value of y in between these two
points so the value of y I make a
guesstimate is somewhere about I'm going
to just say Y is equal to
three-point-six okay so what I did here
estimating between two points is an
example of interpolation okay layouts
well this correctly interpolation okay
because I'm estimating in between two
points okay all righty now so it asks us
for another thing nine point three X is
equal to nine point three so what's the
value of y we look at that our graph
doesn't even go that far
okay so one of the things we have to
assume for in this case is that our
pattern continues as normal and if it
does then you know what there's no
problem in extending our graph a little
bit okay so it might look something like
that
just like that you know what I'll change
the color of that for you guys just so
you see what I added on there okay so I
extended it a little bit just like that
all right now so now again I had to
estimate what nine point three is so
nine point three is going to be
somewhere about here and I'll go up
until I hit the graph and then I go
straight across and I'm going to change
the color of those as well so I'll
change them to red as well
okay so I
across and I can estimate that that's
probably about 5.7 I'll just make it I
guess Y is equal to five point seven
okay so what I had to do here was extend
my graph and estimate again outside the
points that we already had so the exact
what this is called is extrapolation
okay and they say I strap elated my
graph I assume that my pattern continued
to continue with a straight line
therefore I could just say add on to my
graph there okay so I extrapolated my
graph
now there's I sort of thought about how
you could sort of know or sort of relate
what those two things meant and I
thought of this interpolation is
estimating in between two points so in
between these two points where this
extrapolation is estimating by extending
the graph okay or extrapolating the
graph okay so hopefully that makes
things a little bit clearer okay
so just got to keep those in mind all
right let's try one more example so this
is probably more likely example that
you're you're going to face you might be
asked to do that with just x and y but
it's not really any context to that
already so it says Jeff plots the first
four minutes of this morning jog how
long did it take gift jog two minutes so
I'm looking here and I got to find two
minutes here so two minutes it's right
here okay I go up until I hit the graph
and then I go across a change color that
again blue
all ready so I just basically make my
estimate here and that's a little bit
above 350 I'll go 360 okay how long did
it take Jeff how long did it take you to
take Jeff to jog two minutes that makes
no sense how far maybe I didn't I didn't
proofread this list let's fix it now I
don't want to have to do this video over
again just visit that little mistake how
far see how far did Jeff jog in two
minutes that makes a lot more sense
I know assume you guys were looking at
that when I first read it I never saw it
what is he talking about all right
crisis averted
all right so how far did Jeff jog in two
minutes well two minutes is right here
he jogged 360 meters
okay so again this is it within our data
points here though we don't have any
specific data points here this would be
an example of interpolation because
we're estimating basically inside the
data okay within our data now if Jeff
continues at the same pace so we're
assuming that he's going to continue
jogging now in reality probably wouldn't
be able to continue at the same pace how
long would it take Jeff to jog thousand
meters so let's extend our graph a
little bit okay so extend it this far
maybe make it a different color so you
guys can see what I extend it there okay
so thousand meters so we're starting on
the y axis this time because we know he
jogged a thousand meters so thousand
meters and I'm gonna go straight down
over here and if you look there
it's going to take him just short of six
minutes so maybe we can say it's going
to take him five minutes
and 45 seconds or if you wanted to say
it's going to take him five point eight
minutes or some estimate somewhere along
the lines of that okay either one of
those answers will be perfectly fine I
think it's just estimating right that's
the thing you keep in mind you're going
to have a little bit of a ballpark
number that you gotta be in between you
don't want to be in this case this
number you're not going to say six and I
can say five point five you're going to
say somewhere in between they're a
little bit more than five point five a
little bit less than six what's in
between
five point eight five point seven we
fine five minutes and 45 seconds five
minutes and 40 seconds five minutes and
50 seconds would be perfectly fine keep
that in mind guys this is estimating all
right guys so I hope it's clear that
interpolation is estimating in between
two points extrapolating is estimating
by extending the graph okay outside the
data this is inside the data all right
guys I hope this is clear if you got any
questions message me on youtube check
out my websites I'll see you in class